Print Sizing and Resampling

I'm wanting to find some information about print size limitations, and how large I can print in good quality before it really starts to degrade. Let's say I have an older image that I want to pull and print large, and it's 3,888 x 2,592. Well to print a 30x40 @ 250 DPI, I would have to upsample to 7,500 x 10,000. Is 250 DPI even needed at some a large print? How low can you go before a noticeable degrade in quality on a print? Are there any helpful charts out there to aid with recommended DPI at specific print sizes? Is a 30x40 print too large for a 3,888 x 2,592 image?

I'm sure this has been covered many times and I'm overlooking previous threads, so please forgive me bringing up an old topic, lol!